Stern on discounting and risk

One of the crucial issues in any assessment of climate change policy is how to handle discounting and risk. The Stern review (Ch 2) goes back to first principles and gets the main issues exactly right. The reason for both discounting and risk premiums, in economic analysis, is that the marginal value of a dollar of income is lower when we are rich than when we are poor. Hence, we’re prepared to pay for insurance when we are well off in order that it will pay out when we are badly off. Similarly, if we expect income to rise over time, a dollar of income now is worth more, at the margin, than a dollar in the future. The same points are relevant in considering income distribution but this isn’t covered in the parts of the report I’ve read so far.

In addition, there’s a justification for “inherent discounting”, reflecting the fact that some future event (most probably bad, but perhaps good) may mean that “all bets are off” in relation to future consumption levels. Individuals should have reasonably high inherent discount rates, since we may not be around next year, but the appopriate rate for a community is much lower, being confined to the risk of catastrophes like nuclear war.

The Stern review also has a good discussion of probabilities, including the recent literature on problems where there do not exist well-defined probabilities.

The quality of the economics here is very high, and sets a new bar for discussion of these issues.

FYI
Stern relied most on Wigley and Raper’s (2001) sensitivity and Murphy et al’s (2004) sensitivity. Wigley and Raper (2001) fits into Annan’s priors as it is around p~0.95 for a 4.5 degree senstivity. Murphy’s is higher and has values that James Annan objects to, having its p=0.95 point at around 5.5 degrees. Annan and Hargreaves distribution is centred on 2.9 to 3 degrees and is tighter than both those above but has raised its minimum to >2 degrees (v. slight likelihood of being below this).

If one risk-weights with either Wigley and Raper’s or Annan and Hargreaves’s pdfs for sensitivity, the situation in terms of climate risk is serious enough. The conclusions (for this part of Stern’s risk analysis at least) do not rely on heavy weighting of sensitivities above 4.5 degrees. ~3 degrees sensitivity (Annan’s median) is serious enough.

Uncle Milton: its published. If you want the non-draft version it will cost you $9.00. Although, since Annan posted their accepted version, I doubt the final published version will be that different, although I may be wrong. You could also write to Annan – I am sure he’d send you a copy.

Roger Jones: from Box 1, Page 1, Chapter 1 of Stern:

“A warming of 5Â°C on a global scale would be far outside the experience of human civilisation and comparable to the difference between temperatures during the last ice age and today. Several new studies suggest up to a 20% chance that warming could be greater than 5Â°C.”

Presumably included at the start of the report to ensure anyone easily bored at least gets the main message.

Oferchrissakes. Can’t you obsessives move on to the topic of John’s post – discounting and risk in a long term communal framework? John would be quite justified in deleting the same-old-boring comments above from this post.

JQ said: â€œâ€¦The reason for both discounting and risk premiums, in economic analysis, is that the marginal value of a dollar of income is lower when we are rich than when we are poor.â€?

Could the good professor kindly cite his sources for this statement?

My own most up to date textbook defines risk premiums as â€œ additional interest, in excess of the market rate, that a bondholder receives to compensate him for default riskâ€? (Stephen E Landsberg, Price Theory, Thomson 2005, p.721). Joe Stiglitzâ€™s earlier textbook Public Economics, 3rd edition, p.290, states, â€œthe extra amount a risky project must earn to compensate is its RISK PREMIUMâ€?.

Neither mentions lower marginal income utility of the rich than the poor.

Likewise in positive economics, income distribution has nothing to with â€œthe reason for discountingâ€?. The correct explanation is that â€œit is necessary to discount or reduce the value of future benefits (or future costs) to place them on a par with benefits or costs incurred todayâ€? (see ch. 12 Positive Microeconomics, in Begg, Fischer, Dornbusch, Economics, 5th edition, p.188).

Stern justifies his many departures from conventional economic theory in this area with normative (i.e. ethical) concerns about income distribution and the welfare of future generations, and this goes back to his earliest training and first papers as an apostle of the Little-Mirrlees method of cost-benefit analysis, which proposed that current market prices should be replaced by â€œshadow pricesâ€? determined by the superior wisdom of Stern and his mentors. For example, if an irrigation project looked doubtful at current prices of cotton, then fix a shadow price for either the labour cost (zero) or cotton (10 times the market price). The World Bank took this up and the outcome was billions loaned for projects (eg Bura in Kenya) that however high their â€œeconomicâ€? rate of return when using shadow prices all failed to generate the financial returns that would have been needed to pay back the WB had it not enjoyed state guarantees of the borrowing countries. Hence the 3rd world debt crisis and the justification for writing off all loans provided by the Bank. Stern of course escaped any censure for his role in this debacle, and instead went on to his stellar career at the World Bank.

Stern’s methodology misses the real purpose of discounting, which is to determine the opportunity cost of alternative investments. Setting the rate to 0.1 or even 0.0 for evaluating climate change adaptation or mitigation costs is “ethical” according to Stern, but also penny wise and pound foolish. Consider an evaluation of whether it is better to replace coal or gas power with nuclear or solar, using data from Finland and IEA for nuclear, and from Australia’s coal and power industry plus the proposed solar power plant in Victoria, and using Stern’s US$85 per tonne of CO2 as the climate cost averted by reducing CO2 emissions. Using a zero discount rate, both nuclear and solar yield positive net cash flows vis a vis replacing coal, but only solar is cash positive for replacing natural gas (because of the latterâ€™s lower CO2). Using the internal rate of return, nuclear but not solar shows a return higher than the current market opportunity cost of capital (8%) for coal replacement, and both nuclear and solar fail this market test for natural gas replacement. So the correct decision is to replace coal with nuclear, avoid solar and leave natural gas in place. By using Stern’s zero rate and replacing gas with solar because it is cash positive despite a real rate of return of only 0.16 per cent, we forgo the 8 per cent return on the alternative use of those funds which would enable us to fund more replacement of coal by nuclear. Using a zero rate leads to inefficient policy outcomes including lower reduction in CO2 emissions.

Mutatis mutandis, the same considerations apply to a choice between an investment in an income raising project with a return above the current cost of public sector funds (i.e. reflecting a positive discount rate) and a Stern investment in a climate change adapting or mitigating project that passes a zero discount rate test. The first recovers the cost of financing and yields both income and (if desired) replacement cost, the second does not recover the cost of its funding. Moreover Kay and Mirrlees (1975) argued for a HIGH discount rate as the best way to protect the environment from over-exploitation and resource depletion.

Sternâ€™s ethical justification for his 0.1 per cent social discount is based on his serial misunderstandings of Pigou, Ramsey, and Coase. Pigou correctly noted that â€œthis preference for present pleasures does not â€“ the idea is self-contradictory â€“ imply that a present pleasure of given magnitude is any GREATER than a future pleasure of the same magnitudeâ€? (1929, p.25, his emphasis). In other words, in a yearâ€™s time $100 will yield as much â€œpleasureâ€? as $100 does now.
Ramsey missed Pigouâ€™s point with his statement that â€œ[discounting] is ethically indefensible and arises merely from weakness of our imaginationâ€? (1928). Later he appears to have recanted: â€œin time the world will cool (sic!) and everything will die; but that is a long time off still, and its present value at compound interest is almost nothingâ€? (1931, 12). (Hat tip to Price for the quotes, 1993, 101). With no sense of irony, Stern (Review p.47) adopted Ramsey when he based his 0.1 per cent discount rate on an almost 10 per cent probability of the human race being extinct from excessive heat within 100 years. Cheerful chappy! Not even the IPCC (yet) rates the risks from 5C temperature rise in 100 years as implying a 10% risk of total extinction of the human race.
Stern in his own earlier â€œEconomics of Climate Changeâ€? mentioned Coase, but understandably his Review drops Coaseâ€™s basic argument that the kind of Pigou taxes now being proposed in Britain and the EU (e.g. on air travel) are inefficient because they result in maximizing the costs of mitigating external damages (Coase 1990, 180). The proposed taxes on air travel are analogous to Pigouâ€™s proposed liability of operators of steam trains for damages from sparks causing damage to crops and forests along the way. Coase noted that the farmers could move their crops away from the railway line amongst other possibilities for more efficient outcomes. In the case of the alleged huge losses from putative rising sea levels, it may well be more cost-effective to build seawalls in Venice and Bangladesh than to forego the income arising from maintaining energy consumption levels. Moreover we need (as Coase argues at p.142) â€œto compare the total social product yielded by alternative arrangementsâ€?. This neither Stern nor Quiggin (so far) has attempted. Stern for example does not evaluate what allocating one per cent of GDP per annum to income raising investments (instead of to climate change amelioration) would do for GDP. His claim that losses from climate change are already â€œ5 per cent of GDP p.a. now and foreverâ€? is pure persiflage, or is he saying that China would be growing at 15% p.a. now and forever instead of the actual 10% but for climate change? Tim Worstall has already exposed (at TCS) the bogus nature of the 5% prediction, so I do not need to emulate him.

Facing a catastrophic event, such as Katrina, the millionair may tend to insure more
than the homeless person who live on social insurance. The implication may be that the people
with high income would(should) put more attention to the climate change which would
cause catastrophic disaster. And the catastrohpic event’s impact on rich ppl’s utility may be
much larger that that of some small scale business bankruptcy.

With no sense of irony, Stern (Review p.47) adopted Ramsey when he based his 0.1 per cent discount rate on an almost 10 per cent probability of the human race being extinct from excessive heat within 100 years. Cheerful chappy! Not even the IPCC (yet) rates the risks from 5C temperature rise in 100 years as implying a 10% risk of total extinction of the human race.

You’ve missed the point here. This is the risk of extinction from factors other than global warming, the most obvious candidate being nuclear weapons.

BillyMM, the effects you mentioned can be modelled in various ways, including kinks.

JQ said: “Among the many errors in Tamâ€™s latest, I only have time for one”.

That’s a great cop out! If I am in error I have good company in Pigou, Coase, and (on need for non-zero discount rates in cost-benefit analysis in order to avoid the mistakes of the Koran and the Soviet Union), Richard Cooper. The “error” you do mention is nothing of the sort, as it would be preposterous for Stern to recommend a 0.1 discount rate in regard to avoiding cost of climate change on the basis of risk of extinction of the species from nuclear war when he himself insists on “horses for courses” i.e pick the rate for the risk (invalid though that is according to Cooper).

Bur ever anxious for self-improvement, I really would like my “errors” if such they be to be noted and corrected. Over to the time challenged prof!

Tim, I am indeed time challenged, and correcting your errors would be more than a full-time job. In the above posts, you’ve mischaracterised Coase, Pigou and Ramsey, missed the distinction between discounting and inherent discounting, confused levels and growth rates, mixed up default risks and pure risk premiums, and demonstrated ignorance of basic utility theory. Previous attempts to explain and correct your errors have gone nowhere – you haven’t even grasped the very simple point I made about the 0.1 per cent.

If you think you can prove Ramsey wrong (or even demonstrate that Pigou and Ramsey are on opposite sides as you suggest), there’s certainly a high-grade journal article publication in it for you, so why don’t you go ahead and write it up.

JQ: incorrigble as ever! But if you are thinking of submitting your submission to the Stern Review for publication, can I suggest that you check the equations on p.4? It seems to me there is at least one typo, but even after running it either way, it does not appear to yield the outcomes you claim for it.No doubt there is a simple explanation, like Excel unable to multiply? It also seems odd to have the change in welfare as sometimes an absolute number and sometimes a log.

JQ: I did not suggest “that Pigou and Ramsey are on opposite sides”, they did, as evidenced by the respective quotes. Pigou understood that discounting is an exercise that rolls forward year by year; Ramsey did not. When my grandson’s generation comes of age, they will, unless prevented by Stern and JQ, inherit a capital stock and income stream far in excess of mine that enables them to cope with all that the IPCC may throw at them.

The Stern Review is so badly documented that it is hard to understand what they really did.

When I talked to Stern, he said that the utility discount rate of 0.1% per year was because of the risk of human extinction from climate change. If so, Stern’s climate policy scenario is discounted at a lower rate than Stern’s business as usual scenario.

Chris Hope, who build the model used in the Stern review but did not run it, claims that the 0.1% is for other risks of extinction.

The human race has survived for many centuries. It is hard to imagine that the probability of survival is 1 in 10 in this century.